Model Based approach to Predict Boundary Conditions of a Single Cylinder Test Engine GOUTHAM REDDY MURTAZA KHAMBATY

Transkript

1 Model Based approach to Predict Boundary Conditions of a Single Cylinder Test Engine GOUTHAM REDDY MURTAZA KHAMBATY Master of Science Thesis Stockholm, Sweden 206

2 Model Based approach to Predict Boundary Conditions of a Single Cylinder Test Engine by Goutham Reddy Murtaza Khambaty i

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4 Examensarbete MMK 206:62 MFM65 Model Based approach to Predict Boundary Conditions of a Single Cylinder Test Engine Godkänt Examinator Andreas Cronhjort Uppdragsgivare AVL, Södertälje Goutham Reddy Murtaza Khambaty Handledare Andreas Cronhjort Kontaktperson Johan Fjällman Sammanfattning Huvudämnet i denna avhandling är användningen av prediktiva modeller för att styra randvillkor i en encylindrig motor. Encylindriga motorer används i utvecklingen av nya motorer för att studera förbränningskoncept. De utgör en modulär plattform för utveckling av bland annat nya ventilkoncept, förbränningsmetoder, bränsleinsprutningsmetoder och portkonstruktioner. I en produktionsmotor representeras turboaggregatet och motorn av ett kopplat dynamiskt system där motorns driftspunkt bestämmer avgasmottryck och insugstryck. Det är nödvändigt att utföra experiment på encylindriga motorer med rätt insug- och avgasmottryck för att studierna ska vara realistiska. Dessa encylindriga motorer har dock oberoende ventilstyrda insug- och avgassystem där driftspunkten för en produktionsfärdig flercylindrig motor simuleras. Därför finns det ett behov av att använda modellbaserade tekniker för att styra inlopps- och utloppstryck. I denna avhandling har en metod utvecklats för att förutsäga randvillkor med hjälp av en skalad version av den encylindriga modellen tillsammans med en modell av ett turboaggregat. En detaljerad D modell av en encylindrig provcell skapades i AVL Boost. Modellen har sedan validerats med hjälp av mätdata och skalats till en flercylindermodell. En 0D Simulinkmodell har utvecklats utöver D modellen för att jämföra deras användning i en realtidsapplikation. Samtidigt tas det hänsyn till de avvikelser från verkliga processer som sker i båda modellerna. 0D modellen representerar en enkel motormodell för att förutsäga stationär prestanda genom att förutsätta kvasistationär strömning. Motivationen bakom att använda en sådan modell är att de förutsagda medelvärden av inlopps- och utloppstryckspår ger en mer realistisk referensparameter som kan användas för att styra randvillkoren på en encylindermotor. Avgasturbinen har också modellerats i syfte att studera volutets dämpande effekt på det pulserande avgasflödet. Olika extrapoleringsmetoder för turbinmappar studerades där fysiskt baserade algoritmer användes för att extrapolera turbindata. Turbinvolutet och dess effekter på turbinprestanda har diskuterats tillsammans med uppskattning av effektiviteten hos turbinen under ostadiga flödesförhållanden. Dessa modeller har sedan kalibrerats och validerats mot vevaxelupplösta cylindertryck och cykelmedelvärderade parametrar från mätdata som erhållits från den encylindriga provmotorn. De fel och avvikelser mellan 0D- och D modellerna och mätdata identifierades och diskuterades. En styralgoritm baserad på den encylindriga D Boost simuleringen utvecklades för att reglera insug- och avgastryck och jämfördes sedan mellan 0Doch D modellerna för att utvärdera prestanda och noggrannhet. iii

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6 Master of Science Thesis MMK 206:62 MFM65 Model Based approach to Predict Boundary Conditions of a Single Cylinder Test Engine Goutham Reddy Murtaza Khambaty Approved Examiner Andreas Cronhjort Commissioner AVL, Södertälje Supervisor Andreas Cronhjort Contact person Johan Fjällman Abstract The main topic of study in this thesis is the use of predictive models to control the boundary conditions of a single cylinder engine. Single cylinder engines are used to study combustion concepts in the development cycle of new engines. They provide a modular research platform to develop new valve train concepts, combustion methods, fuel injection methods, port designs among other things. In a production engine the turbocharger and engine represents a coupled dynamic system where the operating point of the engine sets the cylinder exhaust back pressure and the inlet pressure. Hence, it is necessary to provide single cylinder engines with correct charged air input and exhaust back pressure for the studies to be realistic. These single cylinder engines however have independent charging systems and valves to simulate the operating point of a production multi cylinder engine. Therefore, there is a need to use model-based techniques to control the inlet and outlet pressure. In this thesis a method was developed to predict the boundary conditions of the single cylinder test engine using a scaled version of the single cylinder model along with a turbocharger model. A detailed D model of the single cylinder test cell was created using AVL Boost. This model was then validated using measured data and scaled to a multi cylinder model. A 0D model, in the Simulink environment, was also developed together with the D model in order to compare their use in real time application. The 0D model represents a simple approach to engine modelling in order to provide steady state performance prediction, assuming quasi-steady flow. The motivation behind using such a model is that the predicted mean values of inlet and outlet pressure traces provide a more realistic reference parameter that can be used to control the boundary conditions in the single cylinder engine. The turbine volute was also modelled in order to capture the dampening effect it has on the pulsating flow. Different turbine map extrapolation methods were also studied and physics based algorithms were used to extrapolate the turbine data. The turbine volute and its effects on the turbine performance have been discussed along with some thoughts on estimating the efficiency of the turbine during unsteady flow conditions. These models were then calibrated and validated against crank angle resolved cylinder pressures and cycle averaged parameters from measured data obtained from the single cylinder test engine. The errors and deviations between the 0D and D model as well as from the measured data were identified and discussed. A control algorithm using the Single cylinder D Boost simulation, as the plant model, was developed in order to control the inlet and exhaust pressures. The algorithms were then compared between 0D model and D model for evaluating the performance and accuracy. v

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8 Acknowledgement The successful completion of the thesis warrants acknowledgment of the various persons who have provided support, encouragement and advice during the last five months. First and Foremost, we would like to thank Johan Fjällman, our supervisor, for his valuable inputs throughout the course of the thesis and for his patience in answering our many questions. Also, for taking time from his work to provide important feedback in the making of this report. We would also like to acknowledge Johannes Andersen, leading the single cylinder test engine, who was one of the key initiator of the project, for his constant support and advice. We extend our gratitude to Ludvig Adlercreutz, for his help during the testing phase and ensuring the proper functioning of the test cell when needed. We deeply appreciate the effort made by Jonas Modin, Manager at Engine design and development, in realizing this thesis opportunity and for providing us with a chance to work with the professional staff of AVL, MTC, Södertälje. We thank our professors Andreas Cronhjort, Per Riseberg and Anders Hultqvist for their support and advice during the early planning stages of the thesis. They have always ensured that they were available during times of need throughout the course of our Masters program at KTH. We would also like to thank Ted Holmberg, PhD student at Internal Combustion Engines, for his advice in model development. We appreciate the support shown by our fellow Master students and friends, Senthil and Robin, for their feedback and inputs to the project, especially during the planning stages. Lastly, we thank all the staff at AVL, Södertälje, especially at the powertrain engineering department, for providing us with a friendly work atmosphere during the period of this thesis. vii

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10 Nomenclature θ Combustion duration ν W pressure wave propagation speed [m/s] A Area [m 2 ] a sound Speed of sound [m/s] b Crank radius [m] C d Discharge Co-efficient C p Specific heat at constant pressure [J/kgK] C s Isentropic exit velocity C pis Piston speed [m/s] D Tip diameter of turbine blade d Pipe diameter [m] F/A Fuel Air Ratio h Specific enthalpy [J/kg] h t Heat transfer co-efficient [W/m 2 ] k Shape parameter k 2 Mode parameter l Connecting rod length [m] m Mass [kg] N Turbocharger shaft speed [rpm] P Power [W] p Pressure [Pa] Q Heat transfer [J] q ev Evaporation heat of the fuel [J] R Specific gas constant [J/kgK] r Compression ratio T Temperature [T] t Time [s] u Specific Internal Energy [J/kg] U Corrected blade tip speed V Volume [m 3 ] W Work done [J] x Mass fraction ix

11 BMEP Brake mean effective pressure [Bar] BSR Blade speed ratio FMEP Friction mean effective pressure [Bar] IMEP Indicated mean effective pressure [Bar] PMEP Pumping mean effective pressure [Bar] Greek Letters α ratio of effective flow area to total η Efficiency γ Ratio of specific heats µ Turbocharger shaft friction coefficient ω Angular velocity [rad/s] φ Fuel-Air Equivalence Ratio ρ Density of gas [Kg/m 3 ] θ Crank angle [rad] Subscripts a Air actual Actual b Burnt bb Blow-by c Cylinder eng Engine ev Evaporating f Fuel f b Burnt fuel o Start of Combustion o Total, stagnation s f Surface sto Stoichiometric ts Turbine total to static tt Compressor total to total x

12 Contents Sammanfattning Abstract Acknowledgment Nomenclature iii v vii ix Chapter. Introduction.. Single Cylinder Test Rigs.2. Background 2.3. Aim of the study 4 Chapter 2. Methodology D Model D Model Experimental Setup 2 Chapter 3. Results and Discussion Model calibration Model validation Turbine performance Single cylinder performance 32 Chapter 4. Conclusion 36 Chapter 5. Limitations 38 xi

13 Chapter 6. Future work 39 Bibliography 40 xii

14 CHAPTER Introduction This section provides a brief insight into the use of Single cylinder test rigs, the hardware involved and some aspects of engine modelling... Single Cylinder Test Rigs The increasingly stringent emission norms and environmental protection policies have increased the demand for engines with improved fuel efficiency and low emissions. In order to achieve this engine manufacturers look towards downsizing engines and more advanced combustion concepts to ensure clean combustion. To maintain the same power output as a bigger engine, turbocharging systems are used. This trend seems to only grow in recent times, as the internal combustion engine strives to compete with modern cleaner electric drives. An essential tool for any engine developer is the use of single cylinder test benches where concepts in early development phases can be tested on a dynamometer long before they make it into the final production engine. These test benches provide a flexible tool to try out new combustion concepts, valve train control methods etc. (AVL 206) Figure.: Single Cylinder test rig (AVL 206) However, optimization of this system is now more difficult due to its complex nature. Hence it is crucial to understand the effects the turbocharger have on the engine

15 and vice versa. Common practices involve extensive engine testing with different turbochargers setups in order to arrive at the best combination. Although this method has proven to be accurate, it s both time consuming and expensive. This expense in time and money can be reduced by eliminating the turbocharger from the test bench and artificially controlling the supplied boost pressure and providing adequate back pressure by means of valves or throttles. This effectively allows any combination of boost pressure and back pressure for an engine operating point. However this is far from the actual scenario in a turbocharged engine where the turbocharger operating point and engine operating point are mutually dependent on each other for a given engine and turbo combination. Hence it is necessary to use a model of a turbocharged engine in order to arrive at sensible boundary conditions, viz. inlet and outlet conditions, to the single cylinder engine. A fully validated model can be useful in predicting engine performance for various turbocharger setups. Also more importantly, a virtual turbocharger can be run in a Hardware in the Loop (HiL) simulation with the test engine to observe variations in engine performance with the turbocharger characteristics..2. Background Single cylinder test rigs are commonly used to study combustion concepts, valve train control among other things. They are mainly used in the development cycle of an engine as a test bench before applying these concepts to production engines. These rigs consist of one cylinder of the multi-cylinder engine under development with the suitable piping and other accessories such as plenums and valves to provide the correct boundary conditions. Turbocharger is simulated by using a compressed air supply and an exhaust throttle to provide the backpressure as a turbine would on the engine Sako et al. (2005). In order to control the boost pressure and back pressure the turbocharger characteristic should be known and the operating point of the simulated turbocharger should be linked to the operating point of the engine. The turbocharger model needs to first be validated before it is used. For this purpose, a 0D or D engine model can be used to predict engine operating characteristics with good accuracy. Payri et al. (20) have shown that 0D models can be used to predict cylinder states with good accuracy when compared to experimental data. They show that some amount of calibration, in terms of choosing suitable constants, of the model is required in order to achieve a good fit. With such models parametric studies on combustion characteristics can be carried out. The 0D model can be extended to include multiple zone burning in the cylinder to predict knock characteristics as studied by Bade Shrestha & Karim (999). A knock criterion was defined and knocking was predicted, even though the relatively simplified models were used. Turbocharger modelling, similar to engine modelling, can be approached in more than one way. Gambarotta et al. (2009) used a 0D model to represent cylinder events, inlet and exhaust manifolds. The model is a combination of filling and emptying (F&E) method and empirical tables. Turbocharger is represented using maps which provide simple lookup table to estimate their performance. These maps are generally provided 2

16 by the manufacturer of the turbocharger and consist of a collection of steady state operating points of the compressor and the turbine. In their study the map data was extrapolated to extend the range of data to match the range of operation of the engine. This is required in all cases where turbocharger maps are used. Dowell & Akehurst (200) showed that there are certain extrapolation methods that provide a more accurate model of the actual turbocharger operation. It is also shown that interpolation methods have to be carefully chosen since the experimental data often contains points that are spaced far apart. The fact that the turbocharger characteristics change nonlinearly with speed adds to the complexity of the model. The Jensen and Kristiensen method of extrapolation is shown to have the best accuracy at low turbocharger speeds Jensen et al. (99b). A combination of smoothing splines and Hermite splines are used for interpolation in this method. Another method to turbocharger modelling as studied by Sorenson et al. (2005) is by the use of Mean Value Models (MVM) which consists of simple physical and empirical equations. These models are shown to have reasonable accuracy in both steady state and transient operation. The main advantage of the MVM models over F&E models is the speed of computation which is essential for HiL simulations. These MVM models are compared to 2D CFD models by Chaudhari et al. (204) and are seen to overestimate the cylinder pressure. However this error decreases with decreasing intake pressure. Another such model suitable for HiL application is discussed by Zhang et al. (203). In this study the air charging system is modelled using steady state maps with some extrapolation. The turbine however is modelled using a D gas dynamic model in order to get better estimate of the back pressure. However, the backpressure could not be accurately applied which explains the deviation of results from the simulation to the experimental results. Exhaust gas back pressure is very critical to engine performance as studied by Kesgin (2005), a D model of the engine was used to study the effect of varying turbine parameters. In most of the studies the exhaust gas is considered to be a steady flow without any pulsations. This is mainly done because of the lack of data on turbocharger unsteady performance. Some of the effects of increased back pressure are an increase in the residual gas quantity, decreased volumetric efficiency and increased pumping losses. The increased residual gas quantity causes changes in the combustion characteristics. The major effects of this are an increase in exhaust gas temperature and combustion duration, but then again, a decreases in NOx emissions and pumping mean effective pressure is observed (Jang et al. 2004). Reduction in pumping loss results in a significant decrease in specific fuel consumption, where as a longer combustion duration causes a drop in combustion efficiency (Tang et al. 203). Increase in back pressure sharply reduces the peak combustion pressure and heat release rate due to higher residual gas concentration (Kim et al. 2003). Increase in the burnt mass fraction also decreases the indicated specific fuel consumption (ISFC). The effects of unsteady flow on the turbine performance using experiments was studied by Capobianco & Marelli (20). It was observed that the pulsating flow had a 3

17 negative effect on the turbine efficiency especially at low frequencies of mass flow pulsation. The efficiency was seen to be 20 30% lower than the steady state efficiency. Also having a waste gated turbine further amplifies these pulsations when opened. This dependency of efficiency on pulse frequency causes a hysteresis in turbine operating condition. This was also seen in a D analysis of the gas exchange carried out by Renberg (2008) on a turbocharged diesel engine. The error in efficiency was also seen to be higher for low mass flow rate conditions in the turbine. It can be seen that the turbine can be more accurately modelled if D boundary conditions are used. D models can provide a better representation of the flow behavior especially if pulsating flow in the exhaust manifold is of importance. De Bellis et al. (204) demonstrate a D model of a turbine using a rotating pipe segment to simulate the turbine. It seen to have better accuracy than standard map extrapolation methods available from commercial D software..3. Aim of the study The boundary conditions to a cylinder such as the pressure at the inlet manifold during the inlet stroke, pressure in the exhaust manifold during the exhaust stroke as well as the temperature of the air drawn in have a very strong impact in the performance of the engine. In the case of a multi cylinder engine, each cylinder in some way are affected by the gas exchange from the other cylinders since they connect to a common intake and exhaust manifold. Adding a turbocharger to the equation adds more parameters which need to be controlled to optimize the gas exchange of the engine. Hence it is important in the case of single cylinder test beds that the test cell is able to accurately simulate the boundary conditions to the single cylinder engine in order to perform studies on the engine which are realistic. In this study a model-based approach has been developed to solving the problem of defining accurate boundary conditions. Starting with a baseline model of the single cylinder engine, this has been scaled up into a 6 cylinder production engine model with a turbocharger. A 0D approximation and a more accurate D model have been developed in order to predict th e. A comparision of both these models for their use in real-time HiL simulation are made and some points on model outcomes and the errors involved are also discussed. The models are developed with an emphasis on accurately modelling the exhaust back-pressure considering the performance of the turbine. The turbine performance is also modelled taking into consideration the effect of unsteady flow on the efficiency of the turbine. The model can then be used as an input to the single cylinder test cell to set the boundary conditions for different operating points. With such a model there is flexibility in the choice of turbine and compressor since the models can be suitably scaled. The single cylinder test engine along with the test cell piping is also modelled in D and used as the plant model to develop a control algorithm. Finally a scheme for controlling the boundary conditions to the single cylinder using the predictive models has been outlined. 4

18 CHAPTER 2 Methodology This section describes the engine and turbocharger models. The algorithms for both the 0D model and D model are outlined. A brief description of the experimental setup is also discussed D Model The 0D model describes the thermodynamic states such as temperature, pressure and mass in a defined control volume. The equations are based on the solution of the conservation equations for mass and energy as described by equations (2.) and (2.2). The well-known Filling & Emptying method is used wherein the different gas exchange systems are approximated to suitable control volumes and the conservation equations are solved for each of these volumes with the appropriate boundary conditions. Figure 2. shows the conservation of mass and energy for a control volume. Figure 2.: Mass and energy balance for a control volume An engine can be approximated into the following control volumes:. Cylinder 2. Intake Manifold 3. Exhaust Manifold 4. After-treatment Piping and chambers 5

19 Mass Conservation: Energy Conservation: dm dt = ( ) ( ) dm dm dt in dt out (2.) d(mu) dt dq s f = dw s f dt dt dm i + h oi i dt (2.2) Ideal gas law: pv = mrt (2.3) 2... Gas state in Control Volumes Equations (2.) and (2.2) have to be modified and applied to the different control volumes to describe the state of the gases in each of them. The main states of interest in each control volume are mass of air (m a ), mass of fuel(m f ), Temperature(T ) and the Volume(V ). Hence an expression of rate of change of each of these states are required which can then be integrated over time to obtain the time evolution of these quantities in each volume. Equation (2.2) can be re-written as: m du dt + udm dt dq s f = dw s f dt dt dm i + h oi i dt (2.4) It is assumed that the contents of each control volume are homogeneous and also the effects of chemical dissociation are neglected. This is done so as to simplify the solution of the energy equation (Watson 982). This is applicable for volumes such as the Manifolds. However, a certain error is introduced when this simplification is applied to the cylinder during the combustion cycle which is discussed in section 3.. With this simplification the specific internal energy in a control volume simply becomes a function of temperature and the air fuel equivalence ratio only. Hence u = u(t,φ) where: φ = (F/A) actual (F/A) sto (2.5) and equation (2.4) becomes: ( ) ( ) u dt u dφ m + m T dt φ dt + u dm dt dq s f = s f dt dw dt dm i + h oi i dt (2.6) 6

20 By combining equations (2.5) and (2.3) an expression for the rate of change of temperature in a control volume can be obtained as: [ dt = RT ( dv dt V dt + dq s f d(m i ) s f dt + h oi u dm ) i dt dt m u ] dφ / u (2.7) φ dt T In engine cycle simulations it is common to express the rate of change of variables with respect to crank angle, then equation (2.6) can be written as: [ dt dθ = RT ( ) dv V dθ + dq s f s f dθ + d(m i ) h oi i dθ udm dθ m u ] dφ / u (2.8) φ dθ T The pressure in each control volume can be obtained from the ideal gas law with the knowledge of temperature, mass and volume of each control volume. From this point on, the rate of change of variables will be expressed with respect to crank angle for the sake of continuity. The crank angle ranges from 0 to 720, where 0 corresponds to intake TDC. Equation (2.) when applied to a control volume and expressed in crank angle resolution can be written as: ( dm dθ = dm ) ( ) dm dθ in dθ + dm f (2.9) out dθ Another simplification in the modelling approach is that, it is assumed that the fuel is injected directly into the cylinder. Also the fuel is burnt as it is injected hence the only two species existing in the volume are air and burnt fuel. A simplified expression for rate of change of equivalence ratio in each control volume can be obtained. From equation (2.5) we have: m f b φ = (2.0) m a (F/A) sto and m = m a + m f b, by combining the two we get φ = Differentiating equation (2.) we get: ( dφ dθ = (F/A) sto [m m f b ] m f b [m m f b ](F/A) sto (2.) dm f b dθ m f b [m m f b ] 2 which can be rewritten as: dφ dθ = + φ(f/a) ( sto + φ(f/a)sto m (F/A) sto [ dm dθ dm ]) f b dθ dm f b dθ φ dm ) dθ (2.2) (2.3) With the application of equations (2.8), (2.9) and (2.3) to each control volume with specific boundary conditions the thermodynamic state of the gas in that control volume can be estimated at each crank angle step. 7

21 2..2. Combustion There exist many different approaches to modelling the combustion process in a cylinder. The simplest of which was proposed by Ivan Wiebe (Wiebe 962). The Wiebe function is a simple expression for the burnt fuel fraction as a function of crank angle. It is given by: [ ( ) ] θ k2 θo x b = exp k (2.4) θ Together with the assumption of complete combustion of fuel as it is added into the cylinder the heat release rate can be effectively modelled by this approach. Some models such as those proposed by Lindstrom et al. (2005); Ibrahim & Bari (2009) are capable of modelling two zone combustion processes and flame speeds, such methods require extensive calibration from known heat release curves and hence for this study the simple sine Wiebe function is used Cylinder wall heat loss The heat loss through the cylinder walls, heads and piston surface are modelled by using the empirical correlation for heat transfer coefficient proposed by Woschni (Woschni 967). The heat transfer rate due to conduction is neglected since convection from surface to coolant dominates the total heat loss. This convective heat loss is given by: dq s f dθ = h ta cyl (T T coolant ) ω where the heat transfer coefficient is expressed as: h t = K p [ ] V sw T re f B 0.2 T 0.53 K 2 C pis + K 3 (p p mot ) p re f V re f Where: K 0.3 K (Compression, Combustion, Expansion) K (Scavenging phase) K 3 0 (Compression and Scavenging phases) K 3 (2.5) (2.6) Gas property relationship The specific internal energy and specific gas constant of the gas mixture in the control volume is dependent on the temperature and the composition of the gas. An accurate estimation can be made with the knowledge of the specific energies of each of the chemical components and their mass fraction, however this would require complex chemical reaction models which are not included in the current study. Hence simple empirical relations proposed by Krieger & Borman (967) are used to estimate the 8

22 specific internal energy and specific gas constant as a function of Temperature(T ) and Equivalence ratio(φ) as shown in equations (2.7) and (2.20). Where: u = 000(K T K 2 T φ) (2.7) K = 92T x0 6 T x0 9 T x0 3 T x0 7 T 5 (2.8) K 2 = x0 2 T 9.5x0 5 T x0 9 T x0 4 T 4 (2.9) R = φ (2.20) Flow through valves The mass flow between each of these control volumes is controlled by means of suitable orifices defined by the quasi-steady nozzle flow equation which is given by dm dθ = C dap ω eng RT ( p2 p ) (/γ) [ 2γ γ ( p2 p ) (γ )/γ ] (2.2) where p 2 is the upstream and p is the downstream pressures. These orifices include:. Intake Valves 2. Exhaust Valves 3. Inlet Throttle 4. Exhaust orifice (Simulate Resistance from after-treatment system) For the Intake and Exhaust valves the area (A valve ) is given by: A valve = πd valve L valve (2.22) The lift (L valve ) varies with crank angle depending on the profile of the cam. These are specified using a look-up table also known as a valve-lift curve. For the current engine the valve lift with respect to crank angle was measured for both the intake and exhaust valves. These are shown in figure

23 0.9 Exhaust Valve Intake Valve 0.7 Normalized Lift Crank Angle (deg) Figure 2.2: Measured Lift Curves The discharge coefficients of the valves also changes with lift and pressure ratio across the valve, although the effect of the latter is negligible. Figure 2.3 show the dependence of discharge coefficient on valve lift. The volumetric efficiency depends strongly on the flow of gases across the valve, hence it is required to use a look-up table for the discharge coefficient versus lift. 0.9 Normalized Discharge Coefficient Forward Intake Valve Reverse Forward Exhaust Valve Reverse Normalized Lift Figure 2.3: Discharge coefficient vs. Lift Cylinder Kinematics An expression for the cylinder volume as a function of crank angle can be obtained from the piston crank geometry as shown in equation (2.23). Figure 2.4 shows the geometry of the piston and crank. 0

24 Figure 2.4: Cylinder motion ( V = V c + 2 (r ) l l 2 a a) + cosθ sin 2 θ (2.23) Where, V c is the clearance volume of the cylinder Turbocharger The Compressor and Turbine are modelled by means of special orifices where the mass flow and efficiency depend on speed and pressure ratios across each device. The most common practice in modelling turbocharger performance is to use maps that define the performance for a given set of inputs. The most common maps relate Pressure Ratio (PR) (or Expansion Ratio (ER) in case of Turbine), mass flow rate (ṁ), rotational speed (N T ) and the isentropic efficiency (η). However the maps provided by the manufacturer of the turbocharger are often limited to a very narrow range of points and almost always require some method of extrapolating the performance to the full operating range of a turbocharged engine. Since the turbochargers are only tested using steady flow the unsteady performance of the turbine and compressor are not captured by the maps. However an important assumption is made which permits the use of these maps in the engine model. Namely that the turbine and compressor under unsteady flow at each discrete time step behaves the same as it would under steady state conditions. It means that under transient operation the turbocharger is assumed to move through a series of steady state points. In the case of the compressor unsteady flow phenomenon like surge is not common occurrence in normal engine operation. Hence, modelling of compressor unsteady performance can be ignored. Special care needs to be taken when extrapolating turbine maps since the turbine is almost always operated by a pulsating exhaust flow. It is all the more important to capture this behaviour under part load conditions where the turbine efficiency is greatly affected by the pulses

25 in the exhaust flow. It should also be noted that the maps are specified with corrected parameters such as corrected mass flow rate and corrected turbocharger speed. This is done in order to normalize the map data to the flow conditions at the laboratory. Compressor ṁ corr = ṁactual p T (2.24) The required compressor power is expressed as: [ ( P c = ṁc ) (γ )/γ pt p2 ] η tt N corr = N actual T (2.25) p (2.26) As mentioned previously the mass flow through the compressor and the efficiency is obtained from pre-defined maps. In this study a generic compressor map is used, with a suitable scaling factor applied on the mass flow rate and efficiency in order to match the experimental data. The map extrapolation was carried using the Boost Turbocharger Tool. Figures 2.5 and 2.6 show the compressor speed and efficiency map. Each map require two inputs and give one output. In this case the Pressure ratio across the compressor and Shaft speed are used as inputs to obtain the mass flow rate and efficiency. The compressor also increases the temperature of the exiting gases and usually an intercooler of air to air or air to water type are used to cool the compressed air which increases the density. The intercooler apart from removing some amount of heat also provides a blockage and causes a pressure drop. In the D model this cooling effect and the pressure drop have been modelled by the use of the standard intercooler element. In the 0D model however the heat transfer rate of the intake manifold is scaled so as to remove heat from the gas in this volume. Compressor Speed Map Pressure Ratio Corrected speed (rpm/k 0.5 ) Corrected Mass flow rate Figure 2.5: Normalised Compressor Speed map 2

26 0.9 Compressor Efficiency Map Pressure Ratio Corrected Mass flow rate Efficiency Figure 2.6: Normalised Compressor efficiency map Turbine In the case of the turbine, extrapolation requires more care than in the case of the compressor. There are several methods available to do this. These methods can be classified as empirical, semi-empirical or physical based methods. The empirical methods, such as those proposed by Sieros et al. (997); Fang et al. (200), use purely mathematical expressions to fit the test data to suitable curves. While these methods produce sufficiently accurate results with simple calculations their validity can be questioned especially since the turbine operating range is far wider than the manufacturers provided data. Since the blade speed ratio of the turbine varies quite a bit during one pulse it is necessary to ensure that the extrapolation of the turbine performance maps, especially the efficiency map, is done in a physically valid manner. Semi-empirical methods such as the one discussed in Jensen et al. (99a); El Hadef et al. (202) are an improvement over purely empirical algorithms. In the 0D and D model a physical based algorithm proposed by Payri et al. (202) is used to extrapolate turbine map data. In the case of the turbine each of the maps take two inputs and provide one output. However, the turbine efficiency is normally taken as a function of the blade speed ratio rather than the pressure ratio. The blade speed ratio is expressed as: BSR = U C s = U ) γ 2C p ( p 2 γ p Where, U = πdn corr, p and p 2 are the upstream and downstream pressures. (2.27) The turbine performance is commonly approximated to flow through the orifice of an isentropic nozzle (Watson 982; Benson et al. 982). The mass flow rate expression is the same as equation (2.2). The effective area (A e f f ) needs to be estimated as a 3

27 function of turbine inputs, such as shaft speed or BSR and expansion ratio. Knowing the effective area for a given operating point, the mass flow rate can be calculated. The relation for A e f f was originally derived by Sanchez et al. (2004) and further simplified by Payri et al. (202) is written as: A e f f = + [( µ R A R + k + BSR 2 D 2 ) ] 2 D 2 ( ) 2 ( ) 2 µr AR (k 2 IER) 2 µ S A ( S ( η ts [k 2 IER] Where, IER = ER+ 2, with ER being the turbine Expansion Ratio k = ( Co C s ) 2 + ( W C s ) 2, and k 2 is a fitting factor. (2.28) )) γ 2 γ From equation (2.2), A e f f was calculated for measured turbine map points. µ R A R, k, µ S A S, k 2 and D 2 D were used a coefficients for fitting. The expression for turbine efficiency derived by Payri et al. (202) is given by: Where, [ η ts = K BSR 2 + K 2 K ] γ 3 BSR (2.29) BSR 2 ) 2 K = 2( D2 D,with D 2 D being the ratio of turbine exducer to inducer diameter ( ) D2 D K 2 = 2 A e f f A o (tan(a BSR + b) + is the reference inlet area at the stator. K 3 = U*2 2C p tanβ 2 ), β 2 is relative rotor exit angle and A o a, b, A o and β were used as fitting parameters. A non-linear regression fitting algorithm (Levenberg-Marquardt) was used in Matlab to fit equation (2.28) and (2.29) to the raw data. Figures 2.7 and 2.8 depict the results after extrapolating the turbine data. The turbine power is then expressed as: Shaft dynamics P t = ṁc p T η ts [ 4 ( p2 p ) (γ )/γ ] (2.30)

28 Corrected Mass flow rate Turbine Speed Map Corrected speed (rpm/k 0.5 ) Expansion Ratio 0 Figure 2.7: Normalised Turbine speed map Efficiency Turbine Efficiency Map Corrected speed) Blade Speed Ratio Figure 2.8: Normalised Turbine efficiency map By balancing the torque from the compressor, turbine and the inertia of the shaft an expression for the speed of the turbocharger shaft can be obtained. ( ) Pt P c J ω = µω (2.3) ω The last term represents the loss of power due to bearing friction, which is approximated as a linear function of speed Implementation in Simulink All the various submodels mentioned above were modelled in Simulink using blocks from the library. A fourth order discretization (Runge-Kutta Method) was used since 5

29 a lower discretization showed some unstable behavior especially during flow reversal between volumes. The crank angle step was set such that the run time was minimized while ensuring accurate representation of the gas states in the various control volumes. Figure 2.9 shows the top level of the simulink implementation. Figure 2.9: Simulink Model A throttle is also added after the compressor in order to restrict the mass flow in part load conditions. A Simple PID controller is used to control the discharge coefficient to set the inlet manifold pressure to the required value as shown in figure 2.0. Figure 2.0: Inlet throttle control A turbine wastegate is modelled which is also controlled by a simple PID controller in order to limit the maximum pressure ratio across the compressor. This way the 6

30 maximum amount of boost pressure can be controlled. The mass of fuel added is set to the stoichiometric value depending on the mass of air drawn into the cylinder D Model D engine simulation is an essential part of engine development. It is both a cost, and time effective method which can also be used to obtain certain data which would be difficult to acquire without performing simulations. In this task AVL Boost, a commercially available D engine simulation software has been used. The conservation equations for mass, momentum and energy are solved at discretized points to obtain the state of the fluid at different time steps. Equation (2.32) is based on the first law of thermodynamics and equation (2.33) defines conservation of mass AVL (204). Figure 2.: Energy Balance of Cylinder d(m c u) dθ = p c dv dθ + dq F dθ dq w dθ h BB dm bb dθ d(m c ) dθ + dm i dθ h i dm e dθ.h q ev h dm ev dθ = dm i dθ dm e dθ dm BB dθ + dm ev dθ 7 (2.32) (2.33)

31 d(m c.u) dα dq F dα Change of internal energy p c. dα dv Piston work dq w dα h BB dm bb dα Blow-by enthalpy flow dm bb dα Fuel Heat input Wall heat losses Blow-by mass flow The combustion model used is the same Wiebe function described in section 2..2 and the cylinder heat transfer model is described using Woschni correlations. There is no pipe flow in a 0D model, whereas in a D model pipe flow is governed by the Euler equation given by equation (2.34). U t + F(U) = S(U) (2.34) x Where the state vector U is given by: ρ ρ.u U = ρ c V T + 2 ρ u2 ρ w j and the flux vector F is given by: ρ u F = ρ u 2 + p u (E + p) ρ w j u in which E is given by: E = c V T + 2 ρ u2 Another important phenomenon which is not observed in the 0D model is pressure wave motions whose propagation over meter is governed by equation (2.35) where a is ν W = 6 n a sound (2.35) a sound = γ R T Predicting unsteady turbine flow performance using steady state turbocharger maps provided by the manufacture is not an accurate approach. A more realistic approach would be to model the volute as a series of pipes and having the unsteady flow control the time to fill and empty the volute, while the rotor, due to it small flow path, can be modelled in quasi-steady state (Winterbone & Pearson 999). Two simulation models were made in Boost, a single cylinder model of the HD gas engine and a multi cylinder model of the production engine with a turbocharger. The 8

32 engine is a 2 liter HD SI gas engine as described in section 2. The single cylinder model is based on a single cylinder of the aforementioned engine along with the test cell tubing and hardware present at AVL, Södertälje in Sweden Multi Cylinder Model The model was built using standard library elements available in Boost. Figure 2.2 shows the graphical representation of the model. An inlet throttle was added after the compressor to control the inlet manifold pressure. In the same manner a wastegate was also added to bypass the flow across the turbine to maintain a desired boost pressure. Both the throttle and wastegate are controlled using standard PID control. The boost model was run as plant model and the controller was implemented in Simulink. Figure 2.3 shows the control logic of the throttle and the wastegate. Figure 2.2: Multi cylinder D model in Boost Single Cylinder Model The single cylinder model was made in order to replicate the behavior of the single cylinder test engine. In order to provide the suitable boundary conditions to the single cylinder engine, it requires inputs from the multi-cylinder model. Also modeling the single cylinder engine along with the test cell piping allows the design of any necessary controllers using the plant model before running Hardware-in-the-loop (HiL) simulations. Figure 2.4 shows the Boost model of the single cylinder engine with the test cell piping. As discussed in section.3 it is necessary to control the throttle and the back pressure valve in order to control the boundary conditions to the single 9

33 Figure 2.3: Boost model used as plant model for control cylinder engine. The reference values for the controller are provided by the multicylinder model. Both 0D and D models were used to compare the performance. The implementation in simulink is shown in figures 2.5 and 2.6. Figure 2.4: Single cylinder test engine D model in Boost 20

34 Figure 2.5: Control using D model Figure 2.6: Control using 0D model 2.3. Experimental Setup The tests were conducted at AVL in Södertälje and the test plan, shown in tables and 2 was developed to ensure that the whole operating range of the engine was covered. Only steady state points were run as the dynamometer used was unable to simulate transient engine operation. A reference point was maintained and run every five measuring points to make sure all sensors and data acquisition system were 2

35 running consistently. A total of 23 points were run and the models were calibrated against 6 of these points, the other 7 points were used to validate the models after calibration. The boundary conditions for the calibration data is obtained from steady state tests done on the production 6 cylinder engine, however only cycle averaged values were known. Table : Measurement points used for calibration Measurement point Engine speed (RPM) Load (%) Table 2: Measurement points used for Validation Measurement point Engine speed (RPM) Load (%) The data acquisition and engine control systems used during the tests are as follows: LabMeas system - controls coolant temperatures, throttle and exhaust backpressure. As well as logging of time-averaged measurement channels. Raptor system - is the engine management system which controls the spark timing and injection timing of individual injectors. 22

36 Indicom system - logs the crank angle resolved channels specified by the user. BoostCon system - controls the inlet air pressure and the inlet manifold temperature. Sensor channels used for model calibration are - Crank angle resolved Cylinder pressures. Crank angle resolved inlet and exhaust pressures measured near the valves Cycle averaged values for calculated burn duration, IMEP. 23

37 CHAPTER 3 Results and Discussion 3.. Model calibration The calibration of the models was performed against measured data obtained from the tests run on the single cylinder test engine. Since the boundary conditions to the single cylinder engine were known at the test points, the calibration of both the 0D and D models was done against measured data. A calibration scheme described in Westin (2005) was used to calibrate the models. The important parameter values against which the models were calibrated were; IMEP, inlet and exhaust pressure trace, inlet and exhaust mass flows and cylinder pressures. Figure 3. shows the process used to calibrate the models Figure 3.: D model calibration scheme The BMEP value given by equation 3.36 was not chosen as calibration parameter as it depends on the FMEP model in the simulation code and can be inaccurate. The main parameters that were used to calibrate both the 0D and D models were scaling factors for cylinder heat loss, Wiebe function constants for heat release curve, Compressor and turbine mass flow and efficiency scaling factors. 24

38 BMEP = IMEP FMEP (3.36) where IMEP is given by IMEP = IMEP net = IMEP gross - PMEP Due to the complex nature of the two models the parameter estimation was not done in a deterministic way but rather through trial and error with an objective to find the best fit for all the measured points. Figures 3.2 and 3.3 show the accuracy of both the 0D models and D models in predicting the IMEP and the maximum cylinder pressures. The simulink model has lower accuracy compared to the Boost model when it comes to predicting both IMEP and the cylinder pressures, which is expected since there are more approximations made in this model to keep the complexity low. However, IMEP is predicted sufficiently good in the Simulink (0D) model compared to the peak cylinder pressures. In the simulink model the gas properties such as specific gas constant and specific heat are kept constant, this leads to a different path followed in the PV diagram than what is seen in the Boost model. Since the peak cylinder pressure only occurs for a very short duration when the change in cylinder volume with respect to time is low, the IMEP value is not greatly affected by these pressures. The 0.9 Data Fit Y = T : R= Data Fit Y = T : R= Predicted Measured (a) 0D Model Predicted Measured (b) D Model Figure 3.2: Regression plot of Predicted vs Measured IMEP (Normalized) pressure curve was matched by varying the Wiebe parameters ( m, a, combustion duration and start of combustion). A 2D map of the start of combustion vs speed was created to ensure the correct ignition time, which enabled us to match the peak cylinder pressure and IMEP fairly accurately. The Wiebe coefficients that were used are: m = 2.8 a = 6.5 DOC = 45 25

39 0.9 Data Fit Y = T : R= Data Fit Y = T : R= Predicted Predicted Measured (a) 0D Model Measured (b) Dmodel Figure 3.3: Regression plot of Predicted vs Measured Peak cylinder pressure (Normalized) Normalized Start of Combustion (BTDC) RPM 000 RPM 200 RPM 400 RPM Boost pressure (bar) Figure 3.4: Start of combustion map Figure 3.5 shows the distribution of predicted values of both models at different speeds. The difference between the predicted and measured values in both models are due the different ways in which both models handle combustion parameters and their scaling with speed. Boost uses a user defined map for Start of combustion and interpolates in between specified points, while the simulink model only uses a linear function to scale the combustion start and duration with speed and boost pressure. The main target here was to match the measured 50% burn duration with that of the model. The use of a defined ignition map for this engine would increase the accuracy of the heat release curves especially in the case of the 0D model. Another reason for the differences in the two models is the fact that the inlet and outlet pressure trace in the 0D model is almost constant with only some fluctuations depending on the filling and emptying of the manifolds. However the Boost model also captures the pressure wave propagations due to opening and closing of valves which in turn affect the inlet and outlet trace. These differences in inlet and outlet pressure trace also affect the IMEP. 26